Problem: Multiply the following complex numbers, marked as blue dots on the graph: $(3 e^{3\pi i / 4}) \cdot ( e^{\pi i / 3})$ (Your current answer will be plotted in orange.)
Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $3 e^{3\pi i / 4}$ ) has angle $\frac{3}{4}\pi$ and radius $3$ The second number ( $ e^{\pi i / 3}$ ) has angle $\frac{1}{3}\pi$ and radius $1$ The radius of the result will be $3 \cdot 1$ , which is $3$ The angle of the result is $\frac{3}{4}\pi + \frac{1}{3}\pi = \frac{13}{12}\pi$ The radius of the result is $3$ and the angle of the result is $\frac{13}{12}\pi$.